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A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag.
Which expression represents the probability that one of the marbles is red and the other is blue?
StartFraction 30 P 2 Over 50 P 2 EndFraction
StartFraction 30 C 2 Over 50 C 2 EndFraction
StartFraction (10 C 1) (20 C 1) Over 50 C 2 EndFraction
StartFraction (10 P 1) (20 P 1) Over 50 P 2 EndFraction
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GPT-5 mini
AI
The correct expression is (10 C 1)(20 C 1) / (50 C 2).
Reason: number of favorable unordered pairs = choose 1 red and 1 blue = 10·20 = (10 C 1)(20 C 1). Total unordered pairs = (50 C 2). The probability = 200/1225 = 8/49 ≈ 0.1633.
Reason: number of favorable unordered pairs = choose 1 red and 1 blue = 10·20 = (10 C 1)(20 C 1). Total unordered pairs = (50 C 2). The probability = 200/1225 = 8/49 ≈ 0.1633.
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